Question

Let a⃗ =4ı^−2ȷ^, b⃗ =−3ı^+5ȷ^, and e⃗ =2a⃗ +3b⃗ . part a write vector e⃗ in component form.

Answer 1

We have been given that:

Vector $\vec{a}=4\hat i-2\hat j$ and $\vec{b}=-3\hat i+5\hat j$.

Component form of a vector implies to write the vector with each individual components.

Now, our vector $\vec e$ is given by

$\vec e =2\vec a+3\vec b$

Now, $2 \vec a=2(4\hat i- 2 \hat j)=8 \hat i -4 \hat j$

and $3 \vec b= 3(-3 \hat i +5\hat j)=-9 \hat i + 15\hat j$

Plugging the values  of $2 \vec a$ and $3\vec b$, we get:

$\vec e = 8 \hat i-4 \hat j-9 \hat i + 15 \hat j=- \hat i+11 \hat j$

So, the vector 'e' in its component form is given as:

$\vec e= -\hat i+11\hat j$